2 degrees of separation

I’ve always been struck by the birthday paradox which shows that the probability of 2 people sharing the same birthday is more likely than it is unlikely (i.e. over 50% probability) with just 23 people in a group, and virtually guaranteed (i.e. 99% probability) in a group of just 57 people.

Similarly, I’ve felt for quite some time our network at 100%Open is suitable large and diverse that pretty much anybody can come to us with any project or problem and we will know somebody who can help solve it or progress it in the right direction.

2 degreesAnd so recently, we’ve prototyped an exercise at various workshops and events called ‘2 degrees of separation’ that has worked so remarkably well that a) I wanted to share it and b) see if anybody can help prove exactly how it works. The way we have run it to date is as follows:

  1. In a room of at least 30 people, ask everybody to think of a project or problem they are working on right now where what would really help them is to be introduced to a specific person or organisation.
  2. Invite people to then take it in turns to shout out the name of who they are trying to reach, and also to briefly introduce themselves (if necessary) and why they want this introduction.
  3. Ask the whole group if anybody knows that person or organisation directly, or might know how to reach them, and if so to raise their hands.
  4. If so, just point them out to each other so they can chat afterwards and repeat the process a few times.

We’ve now done this exercise 3 or 4 times with group sizes varying from about 30 to nearly 100 and every single time we’ve been able to make a productive connection. And whilst I thought it would probably work I am struck how well it has worked so far.

It’s worth saying that we’ve only done this in mixed groups (i.e. with participants from multiple organisations, many of whom don’t know each other very well). I doubt it would work for a similar sized group within a single organisation for example (as their contacts are more likely to know each other). Also, I think it would only work when some trust is already built up in the group/room else people won’t want to just give up their social networks quite so freely. So it’s not the sort of thing you’d do right at the beginning of a workshop for example, but works well towards the end.

And so my request is, can somebody help me ‘do the maths’ as to how this does actually work and the probability associated with it (for different group sizes) along the lines of the stats underlying the birthday paradox above? If so I’d be really grateful and happy to acknowledge your help and mobilise our social network to help you on a project or a problem if we can. And if we can’t I’m pretty sure we’ll know somebody who can.

Anyway, this is all based on Stanley Milgram’s famous concept of 6 degrees of separation which was first conceived in the 1960’s, and apparently Facebook users now have just 3.74 degrees of separation. However based on our recent experience we think it might be down to more like 2 degrees. As Greg Hadfield says “The world isn’t getting smaller, the networks are getting bigger.”


by Roland. Thanks to David for coming up with the idea for the exercise and to Sean for having the courage to try it out for the first time. Image from Stephen McDermott’s blog here.


  1. nice. it would be great to test the assumption that there’s a minimum number for this to work. maybe the number of degrees of separation goes up as the group gets smaller? there were 80 of us at Spring Union last week and we managed to find links for everone (even the govnt of UAE) with only one degree of separation. mind you we were only connecting organisations rather than individuals.

  2. Thanks David. Yes I’d be keen to know the minimum number too but I actually think the diversity of the network is as important if not more important once you get to a minimum group size. Also, I think all you need to do is get to a friendly contact within the organisation and then they can navigate the hierarchy internally.

  3. Talking of Birthdays and degrees of separation. I read this article and the very next email from Facebook is reminding me two people have their birthdays this week.

    A certain Roland Harwood no less on the 16th and Patrick Lambe also on the 16th, who is also involved in Knowledge Management, innovation, Consulting etc. So only one degree of seperation.

    If you ever found yourself down in Singapore Patrick is a delight. his website is http://www.greenchameleon.com/ and the founder of Straits Knowledge. http://www.straitsknowledge.com/

    I bet you you have more degree’s of commonality than even the birthday, you should meet up at the very least

  4. We conducted something similar during our feedback sessions to the participants in a study on middle managers in the NHS and local authorities – a wide range of organisations fall under those headings. It took the format of speed dating – each person spending a limited time talking with each other – publications to follow – but here is a link to our webpage – http://www.leeds.ac.uk/hsphr/research/AUPC/informal-networks.html.

    I think I agree that “the diversity of the network” is key here and the question of why they are all in the same room to begin with. On a different note – other research argues that we have between 7 and 29 degrees of separation http://snacda.wordpress.com/2008/08/04/proof-just-six-degrees-of-separation-between-us/.

  5. Hey Paul. How about that! The next post should be called 1 degree of separation! Thanks for the intro/heads up re Patrick too. Will connect with him separately. All the best, Roland

  6. Hi Steven. Thanks for jumping in on this conversation and again for the excellent image. Look forward to learning more about your session with the NHS and local authorities. My gut feeling, as I said in one of the earlier comments, was that this would work less well for people within a specific organisation (and by extension within the same sector). My gut feeling as you say is that diversity is more important. The network where we prototyped this last Thursday was amongst senior innovation professionals from a wide range of different companies and sectors as well as from public/private organisations, large and small, creative and technical.

    That microsoft research seems interesting but I’m not sure email is the best proxy for communication and trust and also, whilst it’s not that old, a few years is a lifetime in social networks.

    Anyway, great to get your thoughts and thanks again for contributing.

    PS. And have edited the blog to update the incorrect attribution. Thanks for flagging and apologies for the initial error.

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